## Installation loads

This articel describes the various installation loads and how they are calculated.

- self-weight (in air) loads
- pressure (buoyancy) loads
- bending loads
- dynamic drag loads
- shock loads
- point loads
- static drag loads
- temperature loads

Note: According to the principle of superposition, these loads can be added algebraically.

## 1. Self-weight (in air)

The self weight (in air) load is the load imposed on the casing string by gravitational effects. This load depends on the weight per unit length and the suspended length below the point under consideration.

When referring to casing weight, it is common practice to use the API Nominal Unit Weight as defined in API Bull. 5C3. This figure is based on the calculated theoretical weight of a 20 ft length of threaded and coupled pipe divided by its length. Together with the allowable dimensional tolerances, according to API Spec. 5CT, this means that the actual measured unit weight of an individual pipe length may vary from -4% to +8%. However, the design factor will allow for this variation and for the calculation of the self-weight (in air) load the nominal value can be used.

## 1.1 Vertical well

For a vertical well, the string weight in air at any point in the string is simply the product of the nominal weight per foot and the length of casing below that point:

## 1.2 Straight inclined well

For a straight inclined well, consider a section of casing inclined at an angle q to the vertical. The weight of the section is the measured length, L, multiplied by the nominal weight, wn: wnL. The component of this load along the axis of the casing is given by wnL cosq, and must be balanced by the force at surface, Fa. The component of the weight normal to the casing axis, wnL sinq, must be balanced by a reaction force from the borehole wall. L cosq is equal to the true vertical projection of the section ZL.

Thus, for straight but inclined wells, the axial force at surface resulting from the weight of the casing is the product of the nominal weight per foot and the true vertical projection of the casing length. Similarly, for any point along the casing, corresponding to a true vertical depth z, the axial force at that point is the nominal weight multiplied by the true vertical length of the casing below that point;

## 1.3 Curved well

By ignoring the fluid densities and the surface pressures, it can be derived that the axial load due to self-weight at any point, s, along the casing is;

Hence, for any point along the casing, corresponding to a true vertical depth z, the axial force at that point is the nominal weight multiplied by the true vertical length of the casing below that point:

# 2. Pressure (buoyancy)

Buoyancy related loads have been explained as a result of hydrostatic pressures acting on the casing surfaces.

It can be demonstrated that the contribution of the pressure loads to the axial force can be calculated from the vertical projection of the well.

It should be noted that the as landed pressure (buoyancy) load is always calculated from the fluid columns present at the end of the casing cementation. The effect of cement gelation on buoyancy loads are not well known. The design factor takes these unknowns into account.

# 3. Bending load

Bending affects axial force by increasing tension in the outer, convex casing wall and by reducing tension in the inner concave wall. By the principle of superposition, the axial force caused by bending can be added to those due to self-weight (in air) and pressure (buoyancy) loads.

# 4. Dynamic drag

Dynamic drag loads should be estimated using computer software.

The total friction force, Ffric, is the product of the total force normal to the axis of the casing, Fn, and the friction coefficient m. The direction of the total friction force is opposite to the direction of velocity.

The velocity profile at any point of the casing may consist of two components:

- tripping speed
- rotating speed.

In the majority of casing design applications, rotation will not be present, and hence the total friction force will act entirely in the axial direction. This is usually called drag. When the pipe is rotated only, as for a liner cementation with a rotating liner hanger the total friction force will be manifested as torque at surface. There is no axial drag force because there is no movement in the axial direction.

For simultaneous rotation and reciprocation of a liner during a cementation, the size of the axial component of the total friction force (the drag) and the torque will depend on the relative magnitudes of the rotating and reciprocating speeds.

# 5. Shock load

When a casing that is being run into the hole is suddenly obstructed at a point somewhere along the casing, two shock waves will be generated: an upwards travelling compression wave above the contact point and a downwards travelling tension wave below that point. A similar effect occurs when the casing is being pulled out-of-hole and it is suddenly stopped. Then the tension wave will travel upwards and the compression wave downwards. The origin of shock load can be found in for example the spider elevator early closing or the casing string hanging up on a ledge or the casing string jumping off a ledge.

When a casing that is being run into the hole is suddenly obstructed at a point somewhere between the top end and the bottom end of the casing, two stress waves will be generated: an upward travelling compression wave above the contact point and a downwards travelling tension wave below that point. A similar effect occurs when the casing is being pulled out-of-hole and is suddenly stopped. Then the tension wave will travel upwards and the compression wave downwards. In this section the quantification of these shock loads will be addressed followed by a qualitative evaluation of concurrent shock and drag loads

# 6. Point load

A point load is typically that due to a packer set in the casing and to which a tensile or compressive load has been applied. Alternatively, the applied load could be a pressure load, e.g. during a pressure test against a packer. For all these situations the string is only suspended at surface and not yet cemented in place, i.e. there is no fixed end downhole.

# 7. Static drag

These are drag loads which continue to have an influence on the distribution of forces and stresses within the casing after it has stopped moving. Evaluation of these loads requires a knowledge of the movement history of the casing. Subsequent behaviour of the casing depends on the magnitude and direction of these loads. These loads are assumed to be absent in vertical wells. This area of analysis is complex and at present can only be performed by computerised numerical techniques.

# 8. Temperature load

Increased temperature causes the casing to increase in length, and the ability of the casing to move to accommodate this change determines the resulting stresses. In the installation phase, for uncemented casing which is free to elongate, no additional stress will result.

# 9. Maximum installation load

For each point along the string, it must be confirmed that the casing can accommodate the maximum force that the string at that point will have seen during installation. This is best achieved by considering self-weight, buoyancy, and bending first, and then adding shock or drag loads later by the principle of superposition.

Consider a point X in a vertical casing string, an arbitrary distance y from the shoe. As described earlier, the axial force at any point is given by the weight in air of the casing below that point corrected for the pressure (buoyancy) load. As a string is run deeper into a well, and the hydrostatic pressure at the shoe increases, the pressure (buoyancy) load will increase. As a result, since the weight in air below X is constant, the axial force at point X will decrease. The maximum static axial force experienced by any point in the string during installation, therefore, is the force present when that point is at surface.

This holds for a vertical well. For deviated wells, the true vertical projection of the casing length should be used in all calculations.

In a deviated well, or vertical well with localised doglegs, all casing that has to pass through a dog leg must be designed to withstand the bending loads imposed. For each point in the string it is necessary to calculate the sum of the buoyant axial load and the bending load as that point passes through the dogleg. Since the bending load will be constant through the dog leg, the maximum combined load will coincide with the maximum buoyant axial load over the dogleg interval. This latter load will always be at the top of the dogleg interval, when the string is landed.

For a combination string, which will experience different bending loads and will have different tensile capacities along its length, it will be necessary to plot the maximum experienced load line when installing the string to ensure sufficient capacity is present at all depths. This is specially important for the running of liners through high build-up sections into straight inclined sections.

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